Non-verbal number acuity correlates with symbolic mathematics achievement: but only in children

The process by which adults develop competence in symbolic mathematics tasks is poorly understood. Nonhuman animals, human infants, and human adults all form nonverbal representations of the approximate numerosity of arrays of dots and are capable of using these representations to perform basic mathematical operations. Several researchers have speculated that individual differences in the acuity of such nonverbal number representations provide the basis for individual differences in symbolic mathematical competence. Specifically, prior research has found that 14-year-old children’s ability to rapidly compare the numerosities of two sets of colored dots is correlated with their mathematics achievements at ages 5–11. In the present study, we demonstrated that although when measured concurrently the same relationship holds in children, it does not hold in adults. We conclude that the association between nonverbal number acuity and mathematics achievement changes with age and that nonverbal number representations do not hold the key to explaining the wide variety of mathematical performance levels in adults.     

The approximate number system is not predictive for symbolic number processing in kindergarteners

The relation between the approximate number system (ANS) and symbolic number processing skills remains unclear. Some theories assume that children acquire the numerical meaning of symbols by mapping them onto the preexisting ANS. Others suggest that in addition to the ANS, children also develop a separate, exact representational system for symbolic number processing. In the current study, we contribute to this debate by investigating whether the nonsymbolic number processing of kindergarteners is predictive for symbolic number processing. Results revealed no association between the accuracy of the kindergarteners on a nonsymbolic number comparison task and their performance on the symbolic comparison task six months later, suggesting that there are two distinct representational systems for the ANS and numerical symbols.     

Neural signatures of number processing in human infants: evidence for two core systems underlying numerical cognition

Behavioral research suggests two cognitive systems are at the foundations of numerical thinking: one for representing 1-3 objects in parallel and one for representing and comparing large, approximate numerical magnitudes. We tested for dissociable neural signatures of these systems in preverbal infants, by recording event-related potentials (ERPs) as 6-7.5 month-old infants (n = 32) viewed dot arrays containing either small (1-3) or large (8-32) sets of objects in a number alternation paradigm. If small and large numbers are represented by the same neural system, then the brain response to the arrays should scale with ratio for both number ranges, a behavioral and brain signature of the approximate numerical magnitude system obtained in animals and in human adults. Contrary to this prediction, a mid-latency positivity (P500) over parietal scalp sites was modulated by the ratio between successive large, but not small, numbers. Conversely, an earlier peaking positivity (P400) over occipital-temporal sites was modulated by the absolute cardinal value of small, but not large, numbers. These results provide evidence for two early developing systems of non-verbal numerical cognition: one that responds to small quantities as individual objects and a second that responds to large quantities as approximate numerical values. These brain signatures are functionally similar to those observed in previous studies of non-symbolic number with adults, suggesting that this dissociation may persist over vast differences in experience and formal training in mathematics.     

Basic numerical skills in children with mathematics learning disabilities: a comparison of symbolic vs non-symbolic number magnitude processing

Forty-five children with mathematics learning disabilities, with and without comorbid reading disabilities, were compared to 45 normally achieving peers in tasks assessing basic numerical skills. Children with mathematics disabilities were only impaired when comparing Arabic digits (i.e., symbolic number magnitude) but not when comparing collections (i.e., non-symbolic number magnitude). Moreover, they automatically processed number magnitude when comparing the physical size of Arabic digits in an Stroop paradigm adapted for processing speed differences. Finally, no evidence was found for differential patterns of performance between MD and MD/RD children in these tasks. These findings suggest that children with mathematics learning disabilities have difficulty in accessing number magnitude from symbols rather than in processing numerosity per se.     

The relation between subitizable symbolic and non‐symbolic number processing over the kindergarten school year

A long‐standing debate in the field of numerical cognition concerns the degree to which symbolic and non‐symbolic processing are related over the course of development. Of particular interest is the possibility that this link depends on the range of quantities in question. Behavioral and neuroimaging research with adults suggests that symbolic and non‐symbolic quantities may be processed more similarly within, relative to outside of, the subitizing range. However, it remains unclear whether this unique link exists in young children at the outset of formal education. Further, no study has yet taken numerical size into account when investigating the longitudinal influence of these skills. To address these questions, we investigated the relation between symbolic and non‐symbolic processing inside versus outside the subitizing range, both cross‐sectionally and longitudinally, in 540 kindergarteners. Cross‐sectionally, we found a consistently stronger relation between symbolic and non‐symbolic number processing within versus outside the subitizing range at both the beginning and end of kindergarten. We also show evidence for a bidirectional relation over the course of kindergarten between formats within the subitizing range, and a unidirectional relation (symbolic → non‐symbolic) for quantities outside of the subitizing range. These findings extend current theories on symbolic and non‐symbolic magnitude development by suggesting that non‐symbolic processing may in fact play a role in the development of symbolic number abilities, but that this influence may be limited to quantities within the subitizing range.     

Embodied numerosity: Implicit hand-based representations influence symbolic number processing across cultures

In recent years, a strong functional relationship between finger counting and number processing has been suggested. Developmental studies have shown specific effects of the structure of the individual finger counting system on arithmetic abilities. Moreover, the orientation of the mental quantity representation (“number line”) seems to be influenced by finger counting habits. However, it is unclear whether the structure of finger counting systems still influences symbolic number processing in educated adults.In the present transcultural study, we pursued this question by examining finger-based sub-base-five effects in an Arabic number comparison task with three different groups of participants (German deaf signers, German and Chinese hearing adults). We observed sub-base-five effects in all groups, but particularly so for both German groups who use an explicit sub-base-five system in their finger counting habits. It is concluded that bodily experiences – namely finger counting – influence the structure of the abstract mental number representations even in adults. Thus, the present findings support the general idea that even seemingly abstract cognition may at least partially be rooted in our bodily experiences.     

Cognitive correlates of mathematical achievement in children with cerebral palsy and typically developing children

Background . Remarkably few studies have investigated the nature and origin of learning difficulties in children with cerebral palsy (CP). Aims . To investigate math achievement in terms of word‐problem solving ability in children with CP and controls. Because of the potential importance of reading for word‐problem solving, we investigated reading as well. Sample . Children with CP attending either special (n= 41) or mainstream schools (n= 16) and a control group of typically developing children in mainstream schools (n= 16). Method . Group differences in third grade math and reading, controlled for IQ, were tested with analyses of co‐variance (ANCOVAs). Hierarchical regression was used to investigate cognitive correlates of third grade math and reading. Predictors included verbal and non‐verbal IQ measured in first grade, components of working memory (WM) and executive function (EF) measured in second grade, and arithmetic fact fluency and reading measured in third grade. Results . Children with CP in special schools performed significantly worse than their peers on word‐problem solving and reading. There was a trend towards worse performance in children with CP in mainstream schools compared to typically developing children. Conclusions . Impairments of non‐verbal IQ and WM updating predicted future difficulties in both word‐problem solving and reading. Impairments of visuospatial sketchpad and inhibition predicted future word‐problem, but not reading difficulty. Conversely, deficits of phonological loop predicted reading but not word‐problem difficulty. Concurrent arithmetic fact fluency and reading ability were both important for word‐problem solving ability. These results could potentially help to predict which children are likely to develop specific learning difficulties, facilitating early intervention.     

Associations of non‐symbolic and symbolic numerical magnitude processing with mathematical competence: a meta‐analysis

Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra. Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent the strength of these associations differs systematically between non‐symbolic and symbolic magnitude comparison tasks and whether age, magnitude comparison measures or mathematical competence measures are additional moderators. We investigated these questions by means of a meta‐analysis. The literature search yielded 45 articles reporting 284 effect sizes found with 17,201 participants. Effect sizes were combined by means of a two‐level random‐effects regression model. The effect size was significantly higher for the symbolic (r = .302, 95% CI [.243, .361]) than for the non‐symbolic (r = .241, 95% CI [.198, .284]) magnitude comparison task and decreased very slightly with age. The correlation was higher for solution rates and Weber fractions than for alternative measures of comparison proficiency. It was higher for mathematical competencies that rely more heavily on the processing of magnitudes (i.e. mental arithmetic and early mathematical abilities) than for others. The results support the view that magnitude processing is reliably associated with mathematical competence over the lifespan in a wide range of tasks, measures and mathematical subdomains. The association is stronger for symbolic than for non‐symbolic numerical magnitude processing. So symbolic magnitude processing might be a more eligible candidate to be targeted by diagnostic screening instruments and interventions for school‐aged children and for adults.     

Brief non-symbolic,approximate number practice enhances subsequent exact symbolic arithmetic in children

Recent research reveals a link between individual differences in mathematics achievement and performance on tasks that activate the approximate number system (ANS): a primitive cognitive system shared by diverse animal species and by humans of all ages. Here we used a brief experimental paradigm to test one causal hypothesis suggested by this relationship: activation of the ANS may enhance children’s performance of symbolic arithmetic. Over 2 experiments, children who briefly practiced tasks that engaged primitive approximate numerical quantities performed better on subsequent exact, symbolic arithmetic problems than did children given other tasks involving comparison and manipulation of non-numerical magnitudes (brightness and length). The practice effect appeared specific to mathematics, as no differences between groups were observed on a comparable sentence completion task. These results move beyond correlational research and provide evidence that the exercise of non-symbolic numerical processes can enhance children’s performance of symbolic mathematics.     

Effective brain connectivity in children with reading difficulties during phonological processing

Using Dynamic Causal Modeling (DCM) and functional magnetic resonance imaging (fMRI), we examined effective connectivity between three left hemisphere brain regions (inferior frontal gyrus, inferior parietal lobule, fusiform gyrus) and bilateral medial frontal gyrus in 12 children with reading difficulties (M age=12.4, range: 8.11-14.10) and 12 control children (M age=12.3, range: 8.9-14.11) during rhyming judgments to visually presented words. More difficult conflicting trials either had similar orthography but different phonology (e.g. pint-mint) or similar phonology but different orthography (e.g. jazz-has). Easier non-conflicting trials had similar orthography and phonology (e.g. dime-lime) or different orthography and phonology (e.g. staff-gain). The modulatory effect from left fusiform gyrus to left inferior parietal lobule was stronger in controls than in children with reading difficulties only for conflicting trials. Modulatory effects from left fusiform gyrus and left inferior parietal lobule to left inferior frontal gyrus were stronger for conflicting trials than for non-conflicting trials only in control children but not in children with reading difficulties. Modulatory effects from left inferior frontal gyrus to inferior parietal lobule, from medial frontal gyrus to left inferior parietal lobule, and from left inferior parietal lobule to medial frontal gyrus were positively correlated with reading skill only in control children. These findings suggest that children with reading difficulties have deficits in integrating orthography and phonology utilizing left inferior parietal lobule, and in engaging phonological rehearsal/segmentation utilizing left inferior frontal gyrus possibly through the indirect pathway connecting posterior to anterior language processing regions, especially when the orthographic and phonological information is conflicting.     

Both non-symbolic and symbolic quantity processing are important for arithmetical computation but not for mathematical reasoning

This study investigated whether numerical processing was important for two types of mathematical competence: arithmetical computation and mathematical reasoning. Thousand eight hundred and fifty-seven Chinese primary school children in third through sixth grades took eight computerised tasks: numerical processing (numerosity comparison, digit comparison), arithmetical computation, number series completion, non-verbal matrix reasoning, mental rotation, choice reaction time, and word rhyming. Hierarchical regressions showed that both non-symbolic numerical processing (numerosity comparison) and symbolic numerical processing (digit comparison) were independent predictors of arithmetical computation but neither was a predictor of mathematical reasoning (assessed by number series completion). These findings suggest that the cognitive basis of mathematical performance varies depending on the type of mathematical competence measured.     

Sex differences in assertive achievement patterns

Observations in mathematics and social studies classrooms were made of 40 sixth-grade children of average and high ability to investigate whether males and females differ in assertive achievement behavior. The prediction of less assertive achievement behavior for females than males was supported only among average-ability children. Particularly in social studies, average-ability females participated less in the classroom than average-ability males and either high-ability males or females. Average-ability females' deficit of assertive behavior became more pronounced as the behavior category increased in degree of assertiveness. High-ability females demonstrated a deficit only in the most assertive behavior category.     

Atypical neural functions underlying phonological processing and silent rehearsal in children who stutter

Phonological processing was examined in school-age children who stutter (CWS) by assessing their performance and recording event-related brain potentials (ERPs) in a visual rhyming task. CWS had lower accuracy on rhyming judgments, but the cognitive processes that mediate the comparisons of the phonological representations of words, as indexed by the rhyming effect (RE) ERP, were similar for the stuttering and normally fluent groups. Thus the lower behavioral accuracy of rhyming judgments by the CWS could not be attributed to that particular stage of processing. Instead, the neural functions for processes preceding the RE, indexed by the N400 and CNV elicited by the primes and the N400 elicited by the targets, suggest atypical processing that may have resulted in less efficient, less accurate rhyming judgment for the CWS. Based on the present results, it seems likely that the neural processes related to phonological rehearsal and target word anticipation, as indexed by the CNV, are distinctive for CWS at this age. Further, it is likely that the relative contributions of the left and right hemispheres differ in CWS in the stage of processing when linguistic integration occurs, as indexed by the N400. Taken together, these results suggest that CWS may be less able to form and retain a stable neural representation of the prime onset and rime as they anticipate the target presentation, which may lead to lower rhyming judgment accuracy.     

数学焦虑个体近似数量加工的神经机制:一项EEG研究

近似数量加工是对大数目物体数量在不依赖逐个数数前提下的估计。行为学研究提示高数学焦虑人群近似数量加工能力下降, 但神经机制未明。本研究探讨高数学焦虑个体近似数量加工的神经机制, 比较高低数学焦虑脑电活动的差异:(1)行为上无显著组间差异; (2)高数学焦虑组的P2p成分波幅增加; (3) δ频段ERS及β频段ERD无显著数量比例效应, 而低数学焦虑组在上述指标的数量比例效应显著。本研究为高数学焦虑人群近似数量加工能力下降提供了电生理学的证据。     

Neural activation underlying cognitive control in the context of neutral and affectively charged pictures in children

The neural correlates of cognitive control for typically developing 9-year-old children were examined using dense-array ERPs and estimates of cortical activation (LORETA) during a go/no-go task with two conditions: a neutral picture condition and an affectively charged picture condition. Activation was estimated for the entire cortex after which data were exported for four regions of interests (ROIs): ventrolateral prefrontal cortex (VLPFC), dorsal anterior cingulate cortex (dACC), dorsolateral prefrontal cortex (DLPFC), and orbitofrontal/ventromedial prefrontal cortex (OFC/VMPFC). Results revealed faster reaction times, greater N2 activation, and greater prefrontal activation for the affectively charged picture condition than the neutral picture condition. The findings are discussed in reference to the impact of affective stimuli on recruitment of specific brain regions involved in cognitive control.     

Young children's non‐numerical ordering ability at the start of formal education longitudinally predicts their symbolic number skills and academic achievement in maths

Ordinality is a fundamental feature of numbers and recent studies have highlighted the role that number ordering abilities play in mathematical development (e.g., Lyons et al., 2014 ), as well as mature mathematical performance (e.g., Lyons & Beilock, 2011 ). The current study tested the novel hypothesis that non‐numerical ordering ability, as measured by the ordering of familiar sequences of events, also plays an important role in maths development. Ninety children were tested in their first school year and 87 were followed up at the end of their second school year, to test the hypothesis that ordinal processing, including the ordering of non‐numerical materials, would be related to their maths skills both cross‐sectionally and longitudinally. The results confirmed this hypothesis. Ordinal processing measures were significantly related to maths both cross‐sectionally and longitudinally, and children's non‐numerical ordering ability in their first year of school (as measured by order judgements for everyday events and the parents’ report of their child's everyday ordering ability) was the strongest longitudinal predictor of maths one year later, when compared to several measures that are traditionally considered to be important predictors of early maths development. Children's everyday ordering ability, as reported by parents, also significantly predicted growth in formal maths ability between Year 1 and Year 2, although this was not the case for the event ordering task. The present study provides strong evidence that domain‐general ordering abilities play an important role in the development of children's maths skills at the beginning of formal education.     

Academic achievement in children of divorce

The influence of parental divorce on Swedish children's final grades from compulsory school was studied. The study group comprised all children (n = 74) of a 1-year-sample of divorcing parents, who finished school within 1 year before, to 5 years after the parental divorce. Each child was matched with two classmates of the same sex from nondivorced homes, born at approximately the same time (control group). Comparisons of grade point average were made among children with different socioeconomic status. The grades of the children of divorce and the controls were similar, but children of manual workers were found to have a lower grade point average than children of higher level nonmanual employees. Thus, the study indicates that parental divorce in itself does not imply a significantly detoriated outcome in final school grades among children.     

Basic number processing deficits in ADHD: a broad examination of elementary and complex number processing skills in 9- to 12-year-old children with ADHD-C

ADHD (attention-deficit hyperactivity disorder) and academic difficulties are frequently associated, but to date this link is poorly understood. In order to explore which components of number processing and calculation skills may be disturbed in children with ADHD we presented a series of respective tasks to 9- to 12-year-old children with ADHD-combined type and matched children without ADHD (of any type) without concomitant dyscalculia and/or dyslexia. Overall, group differences were not significant regarding overlearned and explicitly trained simple and complex calculation skills. More basic number processing skills are - for instance - the ability to compare one-digit numbers according to their magnitude (so-called magnitude comparison), to count or to transcode numbers, i.e. to write down an Arabic number '21' in verbal dictation. Significant differences favouring control children in basic number processing skills were obtained in a number comparison task and in a dot enumeration task. Importantly, our results cannot be explained by group differences regarding specific working memory and executive function components. Thus, number processing skills and in particular the processing of numerical magnitude should be investigated in children diagnosed with ADHD even when no comorbid learning disabilities are reported.     

Race-based perceptual asymmetries underlying face processing in infancy

Adults process other-race faces differently than own-race faces. For instance, a single other-race face in an array of own-race faces attracts Caucasians’ attention, but a single own-race face among other-race faces does not. This perceptual asymmetry has been explained by the presence of an other-race feature in other-race faces and its absence in own-race faces; this difference is thought to underlie race-based differences in face processing. We examined the developmental origins of this mechanism in two groups of Caucasian 9-month-olds. Infants in the experimental group exhibited a preference for a pattern containing a single Asian face among seven Caucasian faces over a pattern containing a single Caucasian face among seven Asian faces. This preference was not driven by the majority of elements in the images, because a control group of infants failed to exhibit a preference between homogeneous patterns containing eight Caucasian versus eight Asian faces. The results demonstrate that an other-race face among own-race faces attracts infants’ attention but not vice versa. This perceptual asymmetry suggests that the other-race feature is available to Caucasians by 9 months of age, thereby indicating that mechanisms of specialization in face processing originate early in life.